
Archive issue  vol.3 No.2
No. 
Author(s)  Title 
Pages 
1. 
Nsom B.  Stability of TaylorDean flow of fiber suspensions 
185204 
2. 
Gorla R.S.R., Mansour M.A. and ELHawary H.M.  Thermal radiation effects on boundary layer flow on a continuous porous flat surface 
205216 
3. 
Kohr M.  An direct boundary integral equations method to Stokes flow past rigid bodies in ground effect 
217232 
4. 
Ghosh P. and Basu U.  Waves due to initial disturbances at the interface between two superposed fluids 
233247 
5. 
Das S. and Patra B.  Interaction between three line cracks in a sandwiched orthotropic layer 
249269 
6. 
Erdogan E.  Effects of the side walls in generalized Couette flow 
271286 
7. 
ELHakiem M.  Effects of a transverse magnetic field on natural convection with temperature dependent viscosity in micropolar fluids 
287304 
8. 
Slavova A.  Stability analysis of nonlinear cellular neural networks with hysteresis in the output dynamics 
305322 
9. 
Shin S. and Kim B.S.  Numerical heat transfer in a rectangular duct for a nonNewtonian fluid with shear ratedependent thermal conductivity and temperature dependent viscosity 
323337 
10. 
Walicki E. and Walicka A.  Flow of a Vočadlo fluid in a slot between rotating surfaces of revolution 
339358 

1.
STABILITY OF TAYLORDEAN FLOW OF FIBER SUSPENSIONS
Blaise NSOM
Laboratoire de Rhéologie (CNRSUJFINPG)
Domaine UniversitaireB.P. 53X 38041Grenoble, FRANCE
We present a theoretical study of the stability of the TaylorDean flow of
dilute and semi concentrated suspensions of stiff fibers. To this end, we
consider a widegap CouetteTaylor configuration with pressure gradient acting
in the transverse direction. The Ericksen anisotropic fluid equation of state is
used to describe the suspension rheological behavior. The marginal stability
states are computed with respect to three parameters: the gapwidth, the ratio
of representative pumping and rotation velocities and the rheological parameter
h2 (h2 being an explicit function of the fiber aspect ratio (dilute suspension),
concentration and number density (semi concentrated suspension)).

Key words: 
fiber suspension, dilute, semi concentrated, rheological model, instabilities, TaylorDean flow. 
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2.
THERMAL RADIATION EFFECTS ON BOUNDARY LAYER
FLOW ON A CONTINUOUS POROUS FLAT SURFACE
R.S.R. GORLA
Department of Mechanical Engineering
Cleveland State University
Cleveland, OH 44115, USA
M.A. MANSOUR and H.M. ELHAWARY
Department of Mathematics Assiut University
Assiut, EGYPT
An analysis is presented based upon the Chebyshev spectral method for the
boundarylayer flow on a continuous porous flat surface. This technique reduces
the problem to a system of nonlinear equations in the highest order derivatives
which were solved by Newton's iterations.

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3.
AN DIRECT BOUNDARY INTEGRAL EQUATIONS METHOD TO
STOKES FLOW PAST RIGID BODIES IN GROUND EFFECT
Mirela KOHR
University BabesBolyai, Faculty of Mathematics
Cluj  Napoca, ROMANIA
The aim of this paper is to give a direct boundary integral equations method
for the slow motion of some rigid bodies of an arbitrary shape, near a plane
wall in a viscous incompressible fluid. By using an integral representation of
the velocity field as a sum between singlelayer potentials and doublelayer
potentials, the problem is reduced to the study of a Fredholm integral system of
the second kind. By following the properties of the singlelayer and
doublelayer operators, the existence and uniqueness result of the corresponding
solution is given. The numerical results are obtained by a standard boundary
element method.

Key words: 
Stokes flow, Green's function, doublelayer and singlelayer potentials, compact operators, Fredholm's results. 
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4.
WAVES DUE TO INITIAL DISTURBANCES AT THE
INTERFACE BETWEEN TWO SUPERPOSED FLUIDS
Prity GHOSH
Physics and Applied Mathematics Unit,
Indian Statistical Institute
203 B. T. Road, Calcutta 700 035, INDIA
Uma BASU
Department of Applied Mathematics
92 A. P. C. Road, Calcutta 700 009, INDIA
This paper is concerned with generation of interface waves due to an initial
disturbance at the interface between two superposed homogeneous and inviscid
fluids, the lower fluid being of finite depth and the upper fluid extending
infinitely upwards. Assuming linear theory, the problem is formulated as a
coupled boundary value problem in the velocity potentials describing the motion
in the two fluids. The interface depression is obtained when the initial
disturbance at the interface is in the form of a prescribed depression of the
interface or an impulse concentrated at a point. In both the cases, the
interface depression is obtained in terms of an infinite integral which is
evaluated asymptotically for large time and distance. This is then displayed
graphically in a number of figures to visualise the effect of the upper fluid
and also the effect of the finite depth of the lower fluid on the wave motion at
the interface.

Key words: 
superposed fluids, inertial interface, lineariesd theory, initial disturbances, interface depression. 
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5.
INTERACTION BETWEEN THREE LINE CRACKS
IN A SANDWICHED ORTHOTROPIC LAYER
S. DAS and B. PATRA
Department of Mathematics
B.E.College (D.U.)
Howrah  711103, W.B. INDIA
The paper deals with the interaction between three coplanar Griffith cracks
located symmetrically in the mid plane of an orthotropic elastic layer of finite
thickness 2h sandwiched between two identical orthotropic half planes. The
Fourier Transform Technique is used to reduce the elastostatic problem to the
solution of a set of integral equations which have been solved by using the
finite Hilbert transform technique and Cook's result. The analytical expressions
for the stress intensity factors and stress magnification factors at the crack
tips are obtained for large h. Numerical results for stress intensity factors
and stress magnification factors have been illustrated graphically.

Key words: 
interaction, crack, orthotropic, stress intensity factor, stress magnification factor, integral equation, Hilbert transform. 
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6.
EFFECTS OF THE SIDE WALLS IN GENERALIZED COUETTE FLOW
M.Emin ERDOGAN
Instanbul Teknik Üniversitesi
Makina Fakültesi 80191, Gümüssuyu
Istanbul, TURKEY
The effects of the side walls on the flow of an incompressible viscous fluid
in a conduit of rectangular crosssection by the combined effect of the velocity
of the top wall and a constant pressure gradient along the conduit are
considered. For this purpose, four different flow conditions are used. In the
first case, a separation occurs at the bottom wall. In the second case, the
volume flux is zero. In the third case, a separation occurs at the top wall. In
the fourth case, the flow is set up by the motion of the top wall in the absence
of the pressure gradient. Furthermore, the effect of the side walls in a channel
of rectangular crosssection is discussed.

Key words: 
effects of the side walls, viscous fluid, Couette flow. 
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7.
EFFECTS OF A TRANSVERSE MAGNETIC FIELD ON
NATURAL CONVECTION WITH TEMPERATURE DEPENDENT
VISCOSITY IN MICROPOLAR FLUIDS
M. ELHAKIEM
Mathematics Department
Faculty of Science, South Valley University
ASWAN, EGYPT
A regular parameter perturbation analysis is presented to study the effect
of uniform transverse magnetic field with temperature dependent viscosity in
micropolar fluids. Four different vertical flows have been analyzed: these
adjacent to an isothermal surface, uniform heat flux surface, a plane plume and
wall plume. Viscous dissipation, motion pressure and volumetric energy source
effects are neglected. The absolute viscosity 'mi' is taken to be variable in the
force momentum balance while the fluid volumetric coefficient of thermal
expansion, 'beta', specific heat, C_{p} and thermal conductivity, k, are assumed to be
constant. Numerical solutions are obtained for different values of the magnetic
field, material parameters and micropolar parameters.

Key words: 
natural convection, micropolar fluids, magnetic field. 
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8.
STABILITY ANALYSIS OF NONLINEAR CELLULAR
NEURAL NETWORKS WITH HYSTERESIS
IN THE OUTPUT DYNAMICS
Angela SLAVOVA
Department of Mathematics,
University of Mining and Geology
Sofia 1100, BULGARIA
In this work, hysteresis of cellular neural network is investigated. The
general state equation with linear and nonlinear templates is introduced.
Moreover, the output equation is own dynamics where the nonlinearity in the
feedback is allowed to exibit hysteresis. Stability analysis of this cellular
neural network is made. New approach for studying such dynamical systems is
introduced using Lyapunov's majorizing equations.

Key words: 
cellular neural networks, hysteresis, periodic solutions, bifurcations. 
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9.
NUMERICAL HEAT TRANSFER IN A RECTANGULAR DUCT FOR
A NONNEWTONIAN FLUID WITH SHEAR RATEDEPENDENT THERMAL
CONDUCTIVITY AND TEMPERATURE DEPENDENT VISCOSITY
Sehyun SHIN and ByungSuk KIM
School of Mechanical Engineering
Kyungpook National University,
Taegu, 702701 KOREA
The present numerical study investigates the effect of the shear
ratedependent thermal conductivity (SRDC) fluids on the heat transfer
enhancement in a 2:1 rectangular duct flow. An axially and peripherally constant
heat flux boundary conditions (H2) was adopted for a topwallheated
configuration. The present numerical results of Nusselt numbers for SRDC fluid
show the heat transfer enhancement over those of a shear rateindependent
thermal conductivity fluid. The heat transfer enhancement is due to the effect
of the increased thermal conductivity near the wall, which is attributed to the
thigh wall shear rates. The present study proposes a correlation between the
Nusselt number and variable thermal conductivity as follows; ___ . Both the
temperature and shear ratedependencies of the properties play important roles
on the heat transfer enhancement.

Key words: 
shearrate dependent thermal conductivity, temperaturedependent viscosity, heat transfer enhancement. 
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10.
FLOW OF A VOČADLO FLUID IN A SLOT
BETWEEN ROTATING SURFACES OF REVOLUTION
Edward WALICKI and Anna WALICKA
Department of Mechanics, Technical University,
Zielona Góra, POLAND
This paper contains formulae which define such parameters of the steady
laminar flow of a Vočadlo fluid between rotating surfaces of revolution as the
velocity components 'TETA'_{x}, 'TETA'_{teta}, 'TETA'_{y} and pressure p. The quasilinearized equations of
motion of the Vočadlo fluid flow for axial symmetry in the intrinsic curvilinear
coordinate system x, 'teta', y are used. The obtained solutions to the equations of
motion have been illustrated by an example of flow through the slot of constant
thickness between rotating disks and between rotating spherical surfaces.

Key words: 
Vočadlo fluid, surfaces of revolution, rotational inertia effects. 
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